A boundary perturbation interior point homotopy method for solving fixed point problems

Abstract

In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of Rn, which may improve greatly the computational efficiency of reduced predictor–corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper.